Question

The position of both, an electron and a range of helium atom is known within $1.0nm$. Further the momentum of the electron is known within a range of $5.0\times {10}^{-26}kgm{s}^{-1}$. The minimum uncertainty in the measurement of the momentum of the helium atom is:

• A. $50kgm{s}^{-1}$
• B. $80kgm{s}^{-1}$
• C. $80\times {10}^{-26}kgm{s}^{-1}$
• D. $5\times {10}^{-26}kgm{s}^{-1}$

Answer 1

Answer: (D)

$5\times {10}^{-26}kgm{s}^{-1}$

By Heisenberg's Uncertainity principle,

$\Delta x\times \Delta p\ge \frac{h}{4\pi }$

Position of both an electron & a helium atom $=1nm$

Momentum of an electron $=5\times {10}^{-25}kg.m/s$

When the postion of both the electron and helium atom is same then the momentum of helium atom is equal to momentum of an electron.

Momentum of Helium atom $=5\times {10}^{-26}Kg.m/s$.